Method of manufacturing a mono-crystalline silicon ball

ABSTRACT

When a crystalline nucleus generated from an under-cooled silicon droplet is grown up to a mono-crystalline silicon ball, a critical under-cooling ΔT cr  is determined in response to a diameter d of the silicon droplet so as to satisfy the relationships of (d=5 mm, ΔT cr =100K), (d=3 mm, ΔT cr =120K) and (d=1 mm, ΔT cr =150K). A crystal grown up from the crystalline nucleus at an under-cooling ΔT less than the critical under-cooling ΔT cr  is a mono-crystalline silicon ball with high quality free from cracks or twins.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method of manufacturing amono-crystalline silicon ball useful as a substrate for semiconductordevices.

2. Description of the Prior Art

A utility of silicon wafers as representative semiconductor materialbecomes stronger and stronger in correspondence to development andspread of semiconductor devices in various industrial fields. Since asilicon wafer bigger in diameter is profitable for fabrication ofsemiconductor devices with higher production efficiency, silicon wafersof 300 mm in diameter has been used. Production of silicon wafers of 400mm in diameter is also researched. However, the tendency to enlargementof wafers in diameter would be doubtful, accounting the economical pointof view that a plant designed for production of such big wafers is veryexpensive.

There is a concept directed to use a mono-crystalline silicon ball ofabout 1 mm in diameter, on the contrary to enlargement of siliconwafers. In fact, an integrated circuit designed on a surface of such amono-crystalline silicon ball is researched and examined onapplicability as a low-cost next-generation IC to a micro-machine or thelike. A mono-crystalline silicon ball has been produced so far by ahigh-frequency plasma method, a rotary disk method, a gas-atomizingmethod, a water-atomizing method, an argon-arc rotary electrode method,a plasma-arc rotary electrode method, etc. For instance, JP 11-12091 A1discloses a mono-crystalline silicon ball manufacturing method, whereinspheroidal poly-crystalline silicon covered with oxide film is partiallymelted with heat and then re-crystallized to a spheroidal shape whileshifting the molten part.

It is a big problem how to prepare mono-crystalline silicon in aspheroidal shape at a low cost. A manufacturing method, which fulfillsindustrial productivity, has not been established yet. There are manyunknown matters on progress of crystallization together withreproducibility, when a mono-crystalline silicon ball is produced withuse of a drop tube or by an atomizing method, so that many problemsnecessary for improvement of productivity are still unsettled. Thepresent invention is accomplished to overcome the above-mentionedproblems.

SUMMARY OF THE INVENTION

The present invention aims at production of a mono-crystalline siliconball directly from an under-cooled droplet by properly controllingunder-cooling of the droplet. An effect of the under-cooling oncrystallizing the droplet to a spheroidal shape is discovered by theinventors from studies on re-crystallization of an under-cooled droplet.

The present invention proposes a new method, whereby a mono-crystallinesilicon ball is manufactured from under-cooled silicon melt suspending acrystalline nucleus therein under the condition that a criticalunder-cooling ΔT_(cr) is determined in correspondence with a diameter dof a silicon droplet so as to satisfy relationships of (d=5 mm,ΔT_(cr)=100K), (d=3 mm, ΔT_(cr)=120K), and (d=1 mm, ΔT_(cr)=150K)between the critical under-cooling ΔT_(cr) and the diameter d.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph showing an effect of an under-cooling ΔT of a silicondroplet on a growth velocity V of a crystalline nucleus.

FIG. 2A is a photograph showing seeding with a {111} <110>seed crystalof silicon wafer.

FIG. 2B is a view illustrating a model for explanation of seeding with a{111} <110>seed crystal.

FIG. 3 is a photograph of silicon crystallized as a thin plate in aregion I observed with a high-speed video camera.

FIG. 4 is a graph showing an effect of an under-cooling ΔT on normalizedthickness L/2R.

FIG. 5 is a graph showing an effect of a diameter d of a silicon dropleton a critical under-cooling ΔT_(cr) for transition from the region I toII.

FIG. 6 is a microscopic photograph showing a cross-sectional image of asample grown up from a crystalline nucleus generated at an under-coolingΔT less than 26K.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The inventors have researched and investigated on generation of asolidification nucleus from silicon melt, and discovered that growth ofcrystals is differentiated in response to under-cooling of the droplet.The present invention is accomplished on the basis of the newlydiscovered relationship between the under-cooling and the shape of themono-crystalline silicon. A mono-crystalline silicon ball with highquality is produced by properly controlling the under-cooling ΔT incorrespondence with a diameter d of a silicon droplet. Moreover, amono-crystalline silicon ball bigger in diameter can be manufactured,since conditions for mono-crystallization is greatly relaxed.

The other features of the present invention will be apparent from thefollowing example.

EXAMPLE

A silicon sample, which corresponded to a droplet of 5 mm or less indiameter, was prepared by crushing a poly-crystalline silicon block ofpurity 99.999%.

After the sample was located in a chamber, the chamber was evacuated to10⁻⁴ Pa or so by a turbomolecular pump. An atmosphere of the chamber wassubstituted with argon gas having O₂ content controlled less than 0.02ppm, and the argon gas was continuously supplied as such at a constantflow rate. Thereafter, the sample was pre-heated up to a temperature(−1500K), at which silicon turned to a state having enough electricconductivity, by irradiation with CO₂ laser beam. An electro-magneticforce of 200 kHz was impressed on the pre-heated sample. The samplemelted was a small droplet of 5 mm or less in diameter, which wasfloatable due to impression of the high frequency energy.

The levitated droplet was cooled by supply of cooling He gas, while itstemperature was adjusted by controlling power of the laser beam and aflow rate of the cooling He gas. Under these conditions, a crystalgrowth velocity was measured, and a solid/liquid interface was observed.The crystal growth velocity was measured by use of a high-speed videocamera, whose sampling rate was 40,500 frames/second, together with aphoto diode. A shape of the solid/liquid interface was judged fromimages of the video camera.

A levitated droplet with an arbitrary under-cooling was dropped on achilling Cu plate and abruptly solidified thereon. This droplet wassubjected to the observation of interface morphology.

The inventors researched an effect of an under-cooling ΔT on a crystalgrowth velocity V under these conditions. Results, as shown in FIG. 1,prove that the crystal growth velocity V was varied according to theunder-cooling ΔT. It is understood that the under-cooling was dividedinto three regions I-III in response to shapes of a solid/liquidinterface. A plate-like crystal was observed in the region I, a coarsefacet dendrite was observed in the region II, and a fine facet dendritewas observed in the region III.

A crystal growth velocity V was detected by plotting movement of a tipof the plate-like crystal in the region I, movement of a tip of thefacet dendrite in the region II and movement of the solid/liquidinterface, which was estimated as a macroscopic smooth plane, in theregion III. For comparison, a theoretical value of a growth velocity,which was calculated on the basis of an LKT model, is also shown by thesolid line in FIG. 1.

In the LKT model, a total under-cooling ΔT for growth of a single phaseis represented by ΔT=ΔT_(t)+ΔT_(r)+ΔT_(c)+ΔT_(k). In the formula, ΔT_(t)is a thermal under-cooling and replaced by the following formula withthe assumption that the dendrite is rotationally paraboloidal at itstip.${\Delta \quad T_{t}} = {{\frac{\Delta \quad H_{f}}{C_{p}}P_{t}{\exp \left( P_{t} \right)}{E_{1}\left( P_{t} \right)}} \equiv {\Delta \quad T_{hvp}{{Iv}\left( P_{t} \right)}}}$

E₁ is an exponential integral function, and represented by the followingformula.$E_{1} = {\int_{P_{t}}^{\infty}{\frac{\exp \left( {- z} \right)}{z}{z}}}$

P_(t) (=VR/2a₁) is a thermal Peclae's number given as a ratio of aproduct of the growth velocity V with a radius R of the tip of thedendrite to a thermal diffusivity a₁. I_(v) is an Ivantsov's function. Aratio ΔT_(hyp) of a fusion enthalpy ΔH_(t) to a specific heat C_(p)corresponds to a hyper-cooling limit. ΔT_(r) is an under-cooling causedby Gibbs-Thomson effect represented by ΔT_(r)=2Γ/R. A Gibbs-Thomsoncoefficient Γ is given as a ratio σ/ΔS_(f) of an interfacial energy σ toa fusion entropy ΔS_(f).

In an alloy system wherein solute atoms or molecules are re-distributedat a solid/liquid interface, under-cooling caused by deviation ofcomposition shall be taken into consideration. Such the under-coolingΔT_(c) is given by the following formula.${\Delta \quad T_{c}} = {m\quad {c_{0}\left\lbrack {\frac{1}{1 - {\left( {1 - k} \right){{Iv}\left( P_{c} \right)}}} - 1} \right\rbrack}}$

In the formula, m is the slope of a liquidus line, c_(o) is a bulkconcentration, I_(v)(P_(c)) is an Ivantsov's function given by a solutePeclae's number P_(c)(=VR/2D, wherein D is a diffusion coefficient ofthe solute). ΔT_(k) is an under-cooling caused by interfacial kineticsgiven by ΔT_(k)=V/μ (μ is a kinetic coefficient).

Since a product of V and R is given as a function of ΔT from the formulaof ΔT=ΔT_(t)+ΔT_(r)+ΔT_(c)+ΔT_(k), another condition is necessary toseparate V and R from each other. The following criterion, which isbased on a marginal stability criterion formulated by Langer andMueller-Krumbhaar (issued by Acta Metall. 26(1978), 1681), is often usedfor a rough interface. Said criterion is also used in the presentinvention.$\sigma^{*} = {\frac{2\sigma \quad T_{E}C_{p}a_{l}}{\Delta \quad H_{f}^{2}R^{2}V} = \frac{1}{4\pi^{2}}}$

The under-cooling ΔT_(c) can be omitted, in this example directed to agrowth process of a pure material. In this sense, the totalunder-cooling ΔT can be assumed to a sum of the thermal under-coolingΔT_(t), a curvature under-cooling ΔT_(r) derived from Gibbs-Thomsoneffect and a kinetics under-cooling ΔT_(k). On the calculation, acoefficient μ of interface attachment kinetics was used as a parameterto fit measured values to the LKT model.

It is understood from FIG. 1 that the measured values are wellconsistent with the LKT model in the regions I and II, while there isapparent deviation of the measured values from the LKT model in theregion III.

The inventors presumes the reason of such the deviation as follows: Aneffect of an under-cooling on a shape of a solid/liquid interface duringsolidification of silicon melt is different from an ordinary effectduring solidification of close-packed metal, in the manner such that asolid/liquid interface changes from a plate-like crystal or a facetdendrite to a continuous plane in the region III with a highunder-cooling ΔT. A planar orientation of the plate-like crystaldistinctly suggests a singular plane {111} whose growth is controlled byincorporation of atoms to a step.

In actual, progress of crystallization in a plate-like state parallel toa mono-crystalline seed was observed on a surface of a droplet, as shownin FIG. 2, in the case where the droplet was seeded with themono-crystalline seed having a crystal plane {111} and an edge <111>.Epitaxial growth of the plate-like crystal from the seeding positiontoward the inside but not toward the surface of the droplet is suggestedby a discontinuous periphery of the plate-like crystal, as shown in FIG.3. These results prove that a levitated droplet can be crystallized to amono-crystalline state by maintaining such the conditions of epitaxialgrowth.

Although a droplet is solidified to a plate-like state in the region Iquite different from a facet dendrite in the region II, the same modelis available for analysis of a crystal growth velocity in both theregions I and II. Availability of the same model to both the regions Iand II means that a tip of growth (i.e. an edge of a plate-like crystalin the region I and a tip of a facet dendrite in the region II) is roughand consistent with the LKT model. That is, change of the morphologyfrom plate-like crystal to facet dendrite is probably derived fromdestabilizing of the edge of the plate-like crystal or the tip of thefacet dendrite, without transition from lateral growth to continuousgrowth. In other words, solidification from under-cooled silicon meltwith an under-cooling ΔT<200K is derived from crystal growth caused byadsorption of silicon atoms to a planar interface, and there is notransition from lateral growth to continuous growth.

The epitaxial growth means stability at the edge of the plate-likecrystal in the region I and at the tip of the facet dendrite in theregion II. In this sense, conditions for the epitaxial growth shall beclarified in order to promote growth of a mono-crystal from theunder-cooled droplet. The inventors studied progress of plate-likecrystal growth and researched for conditions necessary for stabilizationof the edge of the plate-like crystal and the tip of the facet dendrite.

Semiconductor material such as Si or Ge has the feature that itssolid/liquid interface becomes a facet plane during crystal growth. Thefacet plane is composed of many singular planes with low indices,typically a plane {111} of Si. In the case where facet growth occurs ina semiconductor melt, the growth can be explained by movement of stepson the singular plane. When an under-cooling ΔT is small, a growthvelocity ν along a normal direction is represented by ν=β_(st)pΔT_(k),wherein β_(st) is a kinetic coefficient of a step, and p is astep-density. Since the step-density p is inversely proportional tospacing in the step, it increases as deviation of a planar orientationof an solid/liquid interface from an orientation of the singular plane.

A microscopic shape of a crystalline nucleus is approximated with asphere due to Gibbs-Thomson effect on occurrence of a minute crystallineembryo in an under-cooled liquid. But, a growth velocity isdifferentiated in response to a step-density p in progress of crystalgrowth, when {111} is destined as a singular plane. With the presumptionthat a horizontal interface, on which the step-density p diverges, is arough plane, the crystalline nucleus changes its shape from a sphere toa flat oval and finally to a thin plate of {111}. Consequently,thickness L of the plate-like crystal is represented by the formula (1),wherein d_(n) is a diameter of the crystalline nucleus, and t₀, which isa time period for tracing a sample with the plate-like crystal, isrepresented by the formula (2). $\begin{matrix}{L = {d_{n} + {\int_{0}^{t_{0}}{v{t}}}}} & (1) \\{t_{0} = {{d_{0}/{\mu\Delta}}\quad T_{k}}} & (2)\end{matrix}$

When the step-density p is calculated by a screw dislocation-controlledcrystal growth model represented by the formula (3), the formula (1) isconverted to the formula (4), wherein d₀ is a diameter of the sample, αis a ratio (α=β_(st)/μ, α<1) of a kinetic coefficient β_(st) of the stepto a coefficient μ of interface attachment kinetics. $\begin{matrix}{p = \frac{h_{st}\Delta \quad T_{k}}{19\quad T_{M}\Gamma_{k}}} & (3) \\{{L \cong {\alpha \quad d_{0}p}} = \frac{\alpha \quad d_{0}h_{st}\Delta \quad T_{k}}{19T_{M}\Gamma_{k}}} & (4)\end{matrix}$

The inventors have investigated an effect of an under-cooling ΔT on anormalized thickness L/2R in response to various coefficients μ ofinterface attachment kinetics, and discovered the relationship of thenormalized thickness L/2R with the under-cooling ΔT, as shown in FIG. 4,wherein R is a critical radius of a tip of crystal growth, and adiameter do of a sample is predetermined to 5.0 mm. Since the criterionfor stability of the plate-like crystal was supposed to L/2R<1.0, theratio α was set at 0.2 under these conditions. A critical under-coolingΔT_(cr) from the region I to II was calculated to 100K, well consistentwith measured values.

The formula (4) also expresses that a critical under-cooling ΔT_(cr) fortransition from the region I to II depends on a size of a sample. Theinventors have confirmed from various experimental results that thecritical under-cooling ΔT_(cr) decreases as enlargement of the sample,as shown in FIG. 5. It is understood from FIG. 5 that the criticalunder-cooling ΔT_(cr) for transition from the region I to II increasesin response to minimization of the sample, and is 150K at a diameterd₀=1.0 mm (α=0.2) of the sample.

The above-mentioned results prove that growth of a plate-like crystal of{111} is realized by generation of a crystalline nucleus at anunder-cooling ΔT less than 100K. When such the plate-like crystal isused as a substrate for crystal growth, a levitated droplet can bemono-crystallized. Growth of mono-crystalline silicon is also recognizedin the following example for mono-crystallization of a sample of 5.5 mmin diameter from a levitated droplet with an aspect ratio of 0.95 ormore.

A crystalline nucleus was generated from a droplet at an under-coolingΔT less than 26K, using a seed crystal. A crystal obtained grown up fromthe crystalline nucleus was subjected to sectional observation with amicroscope. Observation results are shown in FIG. 6. Twin was noted intwo places at an upper part with occurrence of fine cracks at thestarting point of twinning. The results suggest that generation of thetwin relaxed stress caused by dilatational expansion at a tip of thecracks. Orientation of the twin was completely consistent with eachother and there is free from any islands, so that crystallizationprogressed epitaxially in total from the seed crystal.

Reduction of a sample in size makes it easy to control an under-coolingΔT, as shown in FIG. 5, and also suppresses occurrence of a twin orcracks caused by dilatational expansion during crystal growth.Accounting these effects, it is forecast that conditions for generationof mono-crystalline silicon is greatly eased by reducing the size of thesample.

EFFECT OF THE INVENTION

According to the present invention as above-mentioned, amono-crystalline silicon ball with high quality is obtained by properlycontrolling an under-cooling ΔT on the basis of a critical under-coolingΔT_(cr) in correspondence to a diameter d of a silicon droplet, withoutoccurrence of cracks or twin which originates in dilatational expansionduring crystal growth. Since the mono-crystalline silicon ball ismanufactured with high reproducibility, a semiconductor material isoffered as a low-cost next-generation IC.

What is claimed is:
 1. A method of manufacturing a mono-crystallinesilicon ball, which comprises: generating a solidification nucleus froman under-cooled silicon droplet by controlling an under-cooling ΔT onthe basis of a critical under-cooling ΔT_(cr) in correspondence with adiameter d of the silicon droplet; and growing mono-crystalline siliconto a sphere shape from the solidification nucleus at the under-coolingΔT less than the critical under-cooling ≢T_(cr).
 2. A method ofmanufacturing a mono-crystalline silicon ball, which comprises:generating a solidification nucleus from an under-cooled silicondroplet, under the condition that a critical under-cooling ΔT_(cr) isdetermined in response to a diameter d of said silicon droplet so as tosatisfy the relationships of (d=5 mm, ΔT_(cr)=100K), (d=3 mm,ΔT_(cr)120K) and (d=1 mm, ΔT_(cr)150K) between said criticalunder-cooling ΔT_(cr) and said diameter d; and growing mono-crystallinesilicon to a sphere shape from said solidification nucleus at anunder-cooling ΔT less than said critical under-cooling ΔT_(cr).